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    Evaluate some limits

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    Provide some guidance in approaching the following question:

    let c denote a complex constant
    then show that :
    lim (z^2 + c) = z0^2 +c
    z->z0.

    © BrainMass Inc. brainmass.com October 10, 2019, 4:50 am ad1c9bdddf
    https://brainmass.com/math/real-analysis/evaluate-limits-479461

    Solution Preview

    Proof. Let z=x+iy, z0=x0+iy0 and c=a+ib. Suppose that f(z)=u(x,y)+iv(x,y), where u(x,y) and v(x,y) are real functions in terms of x and y. Then

    lim f(z) = lim u(x,y)+iv(x,y) ............................(1)
    z->z0 ...

    Solution Summary

    The solution assesses limits of complex functions.

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